AN IMPROVED ASSUMED STRAIN SOLID SHELL ELEMENT FORMULATION WITH BUBBLE FUNCTION DISPLACEMENTS

A set of four-node solid shell element models based on the assumed strain formulation is considered here. The present study investigates the use of bubble function displacements and the assumed strain field. Careful selection of the assumed strain terms generates an element whose order of numerical integration does not increase even when the bubble function displacements are added. Results for the four-node element without any bubble function terms show sensitivity to element distortion. Use of the bubble functions greatly improves element performance.

[1]  H. C. Park,et al.  A local coordinate system for assumed strain shell element formulation , 1995 .

[2]  T. Hughes,et al.  Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element , 1981 .

[3]  Atef F. Saleeb,et al.  A quadrilateral shell element using a mixed formulation , 1987 .

[4]  K. Bathe,et al.  A continuum mechanics based four‐node shell element for general non‐linear analysis , 1984 .

[5]  L. Morley Skew plates and structures , 1963 .

[6]  D. Talaslidis,et al.  A Simple and Efficient Approximation of Shells via Finite Quadrilateral Elements , 1982 .

[7]  Peter M. Pinsky,et al.  A mixed finite element formulation for Reissner–Mindlin plates based on the use of bubble functions , 1989 .

[8]  Ekkehard Ramm,et al.  EAS‐elements for two‐dimensional, three‐dimensional, plate and shell structures and their equivalence to HR‐elements , 1993 .

[9]  M. Crisfield A four-noded thin-plate bending element using shear constraints—a modified version of lyons' element , 1983 .

[10]  Richard H. Macneal,et al.  Derivation of element stiffness matrices by assumed strain distributions , 1982 .

[11]  Jr. N. Knight The Raasch challenge for shell elements , 1996 .

[12]  S. Lee,et al.  An eighteen‐node solid element for thin shell analysis , 1988 .

[13]  O. C. Zienkiewicz,et al.  A robust triangular plate bending element of the Reissner–Mindlin type , 1988 .

[14]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model , 1990 .

[15]  R. L. Harder,et al.  A proposed standard set of problems to test finite element accuracy , 1985 .

[16]  Ferdinando Auricchio,et al.  A triangular thick plate finite element with an exact thin limit , 1995 .

[17]  E. Ramm,et al.  Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept , 1994 .

[18]  E. Stein,et al.  An assumed strain approach avoiding artificial thickness straining for a non‐linear 4‐node shell element , 1995 .

[19]  Chahngmin Cho,et al.  An efficient assumed strain element model with six DOF per node for geometrically non‐linear shells , 1995 .

[20]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .